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Important Formulas for CAT 2024 Quantitative Aptitude Preparation

Important Formulas for CAT 2024 Quantitative Aptitude Preparation

Edited By Himanshu Shekhar | Updated on Jul 09, 2024 05:55 PM IST | #CAT

Important Formulas for CAT Preparation: Formulas are crucial aspects of CAT exam preparation. So let's get familiar with the importance of CAT formulae and some important CAT formula sheet crucial for CAT exam preparation. When it comes to CAT preparation for the Quantitative Aptitude (QA) section, the most important thing is remembering the formulas and how to apply them in an actual CAT exam. It will help to solve the questions with accuracy and speed.

Here, we have mentioned all the important formula for CAT 2024 along with the important CAT Quantitative Aptitude formulas. Also, over the internet and in recommended CAT preparation books, CAT formula cheat sheet are available which a candidate can use during their preparation. Also, candidates are required to keep revising the following CAT quant formulas from this CAT formula sheet right before the examination.

Important Formulae for CAT 2024 - Quantitative Ability Section

Check out below the CAT formulas for quantitative aptitude. In this article, we have also attached a CAT Formulas pdf file to help candidates revise CAT formula sheet easily.

CAT 2024 Basic Mathematical Formulas

  • (a + b)² = (a² + b² + 2ab)
  • (a – b)² = (a² + b² – 2ab)
  • (a + b)(a – b) = (a² – b²)
  • (a + b)² = (a² + b² + 2ab)
  • (a³ – b³) = (a – b)(a² + ab + b²)
  • (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
  • (a³ + b³) = (a + b)(a² – ab + b²)
  • When a + b + c = 0, then a³ + b³ + c³ = 3abc
  • (a³ + b³ + c³ – 3abc) = (a + b + c)(a² + b² + c² – ab – bc – ac)
  • (a + b)n = an + (nC1)an-1b + (nC2)an-2b² + … + (nCn-1)abn-1 + bn
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Important formula for CAT Number System

  • (1² + 2² + 3² + ….. + n²) = n ( n + 1 ) (2n + 1) / 6
  • 1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2
  • (1³ + 2³ + 3³ + ….. + n³) = (n(n + 1)/ 2)²
  • Sum of first n odd numbers = n²
  • Sum of first n even numbers = n (n + 1)

CAT 2024 Syllabus PDF (Free Download)
This CAT exam 2024 syllabus pdf has detailed section-wise and subject-wise syllabus and important topics of CAT.
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Formulas for LCM and HCF

  • LCM × HCF = Product of the Numbers
  • LCM of Co-prime Numbers = Product Of The Numbers
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Mathematical Formulas for Profit, Loss, and Discount

  • Profit % = Profit/(C P)×100
  • Profit/Gain = (S.P.) – (C.P.)
  • C P = 100/(100+gain %)×S P
  • S P = (100+gain % )/100 ×C P
  • Loss % = Loss/(C.P.)×100
  • Loss = (C.P.) – (S.P.)
  • C P = 100/(100-loss %)×S P
  • S P = (100-loss %)/100×C P

Important formula for CAT Percentages Topic

Find what percentage of X is Y: Y/X x 100

  • Increase N by S% = N(1+S/100)
  • Decrease N by S% = N(1 - S/100)

Important Formulas for Speed, Time, and Distance

  • Speed= Distance/ Time
  • Distance= Speed x Time
  • Time= Distance/ Time

Time and Work Formulas (Basic Formulas)

  • If X can do a piece of work in ‘n’ days, then X’s 1 day’s work= 1/n

  • If X’s 1 day’s work= is 1/n, then X can finish the work in n days.

Averages Formula

Average= Sum of observations/ Number of observations

Simple and Compound Interest Formula

  • Simple Interest: P x i x n (P= Principle, i= interest rate and n= term of the loan)
  • Compound Interest:
    • Compound Interest = [P(1+i)n] - P

    • Compound Interest = P[(1+i)n-1]

Mathematical Logarithm Formulas

  • If n and a are positive real numbers, and a is not equal to 1, then If ax = n, then log a n = x
  • log of 1 to any base is 0 (log b 1 = 0)
  • log of any number to base as itself is 1, log a a = 1
  • The logarithm of a Product (log a pq = log a p + loga q)
  • The logarithm of a Fraction (log a (p/q) = log a p – log a q)
  • log a pn = n log a p
  • a(log a p) = p
  • Base Change Rule of Logarithms: (log a n = log b n × log a b)

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CAT 2024 Trigonometry Formulae

Apart from basic Mathematics fundamental formulas check out some CAT Quant formula cheat sheet for the trigonometry part given below.

  • Trigonometric Identities

    • Sine=Opposite/Hypotenuse

    • Secant=Hypotenuse/Adjacent

    • Cosine=Adjacent/Hypotenuse

    • Tangent=Opposite/Adjacent

    • Co−Secant=Hypotenuse/Opposite

    • Co−Tangent=Adjacent/Opposite

  • The reciprocal identities are given as

    • CosecΘ=1/sinΘ

    • secΘ=1/cosΘ

    • cotΘ=1/tanΘ

    • sinΘ=1/CosecΘ

    • cosΘ=1/secΘ

    • tanΘ=1/cotΘ

Mathematical Mensuration Formulas

  • Rectangle

    • Area = lb

    • Perimeter = 2(l+b)

  • Square

    • Perimeter = 4a

    • Area = a×a

  • Triangle

    • Area =b×h/2 or √s(s-a)(s-b)(s-c)___where s=a+b+c/2

  • Cube

    • Volume: V = l3

    • Surface Area: S = 6s2

    • Diagonal (d) = √3l

    • Lateral surface area = 4a2

  • Circle

    • Circumference = 2πr or πd

    • Area = πr² or πd²/4

    • Area of a sector of a circle = (θπr² )/360

  • Cuboid

    • Total surface area = 2 (lb + bh + hl) or 6l2

    • Volume of cuboid: lbh

    • Length of diagonal =√(l²+b²+h²)

Mixtures and Allegations

If two ingredients are mixed, then

(Quantity of cheaper / Quantity of dearer) = (C.P. of dearer – Mean Price / Mean price – C.P. of cheaper)

Coordinate Geometry

The Distance Between two Points A and B:

  • AB² = (Bx – Ax)² + (By – Ay)²

The Midpoint of a Line Joining Two Points

The midpoint of the line joining the points (x1, y1) and (x2, y2) is:

  • [½(x1 + x2), ½(y1 + y2)]

The Equation of a Line Using One Point and the Gradient

The equation of a line that has gradient m and which passes through the point (x1, y1) is:

  • y – y1 = m(x – x1)

Read more;

Important Formulae for CAT 2024: Surds and Indices


Law of Indices

i. am × an = a(m+n)

ii. (am) / (an) = a(m-n)

iii. (am)n = a(m n)

iv. (a b)n = an bn

v. (a / b)n = an / bn

vi. a0 = 1

Surds

Surds:

Let a be a rational number and n be a positive integer such that a^(1/n) = √[n]{a}. Then, √[n]{a} is called a surd of order n.

Laws of Surds:

i. n√[a = a(1/n)

ii. n√ab = n√a× n√b

iii. n√a/b = n√a / n√b

iv. (n√a)n = a

v. mn√a = mn√a

vi. (n√a)m = n√am

Mixtures and Allegation Formula

If 2 ingredients are mixed, then

  • (Quantity of cheaper/ Quantity of dearer) = (C.P of dearer - Mean price/ Mean price - C.P of cheaper)

Know more on;

Permutation and Combination Formulae for CAT Permutation Formula

Permutations: nPr = n! / (n - r)!

Combinations: nCr = n! / [(n - r)! r!] = nPr / r!

  • Formulas for Set Theory and Function

  • (A ∩ B) ‘ = A’ U B’ and (A U B)’ = A’ ∩ B’f

B-School Accepting CAT Scores: Location-wise

Important Formula for CAT Preparation in 2024

The questions in the QA section are from various topics such as Profit, Loss and Discount, Number System, Time and Work, LCM and HCF, Logarithm, Averages, Set theory and function, Probability, Permutation and combination, Trigonometry, Mensuration, Coordinate Geometry, etc. All formulas for Quantitative Aptitude are the basic and indispensable part of CAT revision tips that will help candidates ace the quantitative section in the CAT 2024 exam.

CAT important formulas act as an elixir to doing excellent in the QA section. So as aspirants start their CAT preparation 2024, here is the list of important formulas that a candidate must master in order to crack the Common Admission Test with a high score.

Know how the CAT score vs percentile is calculated.

Frequently Asked Question (FAQs)

1. How do I start my CAT preparation for 2024?

For CAT preparation 2024, candidates must start their preparation with proper analysis and understanding of the CAT exam pattern and syllabus. They should devise the CAT study plan and focus on important topics to cover them within the stipulated time. 

2. Is 1 month enough for CAT preparation?

CAT preparation requires a significant amount of time to prepare. However, candidates can prepare the CAT exam syllabus within 1 month if the right strategy and determination are executed. 

3. What is the formula for probability in CAT?

CAT Probability or Chance: Probability is a quantitative measure of the likelihood of a particular event occurring. PE=n(E)/n(S), where n(E) = number of favorable events; n(S) = sample space.

4. What is the important formula for percentage in CAT exam?

Important percentage formulas for CAT exam are:

  • Increase N by S% = N(1+S/100)
  • Decrease N by S% = N(1 - S/100)
  • Percentage Change=(New Value−Old Value/Old Value)×100

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Questions related to CAT

Have a question related to CAT ?

Hello aspirant,
The CAT exam syllabus is not officially prescribed, but it generally includes topics from the following sections:

1. Verbal Ability and Reading Comprehension (VARC)
2. Data interpretation and logical reasoning
3. Quantitative ability

  • Arithmetic

  • Algebra

  • Geometry and Mensuration

  • Number System

  • Modern Math

It seems unlikely that you would be able to get admission in the BTech CS branch at BIT Sindri or Mesra with a CML rank of 2058 and category rank of 433.

Key points:

1. The search results indicate that a CML (Common Merit List) rank of 2058 is quite low for admission to premier engineering colleges like BIT Sindri or NIT Mesra.

2. The cutoff ranks for BTech CS branch at these institutes are usually much higher, often in the range of 1000-2000 for the general category.

3. With a category rank of 433, you may have a better chance of getting admission in the reserved category quota, but the competition is still quite high.

4. The search results do not provide specific cutoff details for BIT Sindri or NIT Mesra, but the general trend suggests your current ranks may not be sufficient for the CS branch in these institutes.

My advice would be to:

1. Check the latest cutoff ranks and admission criteria on the official websites of BIT Sindri and NIT Mesra.

2. Explore other options like state-level engineering colleges or NITs where your current ranks may have a better chance of securing admission.

3. Consider improving your performance in the next attempt of the entrance exam to increase your chances of getting into your desired BTech program.



For VARC, read daily from diverse sources (newspapers, novels, journals) to improve comprehension and vocabulary. Practice RC passages and verbal ability questions regularly. For DILR (Data Interpretation and Logical Reasoning) and QA (Quantitative Aptitude), solve previous years' papers and take mock tests to identify weak areas. Join a coaching institute or online courses for guidance and stay consistent with your study schedule. Review and analyze your performance in mocks to understand mistakes and improve. Maintain a positive mindset and stay disciplined in your preparation.

Hello aspirant,

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1-radian measures 600. (True/False)

Option: 1

True


Option: 2

False


$111111^2$ = 

Option: 1

123456654321


Option: 2

123454321


Option: 3

123454321


Option: 4

12345654321


1111112 =___________ 

Option: 1

 123456654321


Option: 2

1234554321


Option: 3

123454321


Option: 4

12345654321


159702 is divisible by

Option: 1

7


Option: 2

9


Option: 3

11


Option: 4

6


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What best can be said about the number of satellites serving C? 

Option: 1

Must be between 450 and 725 

 


Option: 2

Cannot be more than 800 
 


Option: 3

Must be between 400 and 800 

 


Option: 4

Must be at least 100 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What is the minimum possible number of satellites serving B exclusively? 

Option: 1

100


Option: 2

200


Option: 3

500


Option: 4

250


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S? 

Option: 1

At most 475 

 


Option: 2

Exactly 475 
 


Option: 3

At least 475 

 


Option: 4

No conclusion is possible based on the given information 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

 If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE? 

Option: 1

The number of satellites serving C cannot be uniquely determined 

 


Option: 2

The number of satellites serving B is more than 1000 
 


Option: 3

All 1600 satellites serve B or C or S 

 


Option: 4

The number of satellites serving B exclusively is exactly 250 


2839155 is divisible by

Option: 1

2


Option: 2

7


Option: 3

55


Option: 4

None of the above


'a' for which x^{2}-ax+9= 0 can be written as square of a linear factor is

Option: 1

6


Option: 2

-6,6


Option: 3

\left ( 6,\infty \right )


Option: 4

\left ( -\infty,-6 \right )


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